A company produces two products, Product A$,$ which sells for $$210$ per unit, and Product B$,$ which sells for $$270$ per unit, using three activities: Design, which uses engineering hours as the cost driver; Machining, which uses machine hours as the cost driver; and Inspection, which uses the number of batches as the cost driver. The cost of each activity and usage of the cost drivers are as follows:

$\backslash$table$[[,,$Usage by$,$Usage by$],[$Activity Pool $($Driver$),$Cost of Pool,Product A$,$Product B$],[$Design $($engineering hours$),$$$150,000,290,210],[$Machining $($machine hours$),500,000,1,360,2,640],[$Inspection $($batches$),30,000,18,42]]$

The company manufactures $10,000$ units of Product A and $8,280$ units of Product B per month. Each unit of Product A uses $$32$ of direct materials and $$38$ of direct labor, while each unit of Product B uses $$84$ of direct materials and $$44$ of direct labor.

Required:

a$.$ Calculate the Design activity proportions for Products A and B$.$

b$.$ Calculate the Machining activity proportions for Products A and B$.$

c$.$ Calculate the Inspection activity proportions for Products A and B$.$

d$.$ Determine the indirect costs assigned to Product A$.$

e$.$ Determine the indirect costs assigned to Product B$.$